The quality of anchor bolt anchoring in soil sites is usually tested using the acoustic stress wave method. However, at present, there is still a lack of theoretical research on this technology based on the soil site anchoring system. A simplified model of a glass fiber reinforced polymer (GFRP) anchor embedded in earthen material was developed. An analytical expression describing the particle motion response at the free end of the anchor rod under excitation was derived and subsequently validated through laboratory experiments. The difference curve between simulated and measured signals effectively highlights reflected disturbances within the signal. By analyzing the periodicity of these reflections, disturbance types can be classified, thereby enhancing the accuracy of anchor length estimation in earthen sites. The parameter analysis indicates that the initial response of the anchor solid at the soil site is most significantly influenced by the diameter and length of the anchoring section. The vibration frequency has a non-linear inverse relationship with the diameter of the anchoring section, but is most affected by the equivalent elastic coefficient, which is larger, the higher the frequency. The signal attenuation is most affected by the equivalent viscous coefficient, and a larger coefficient leads to rapid signal attenuation. This research work has significant guiding significance for the quality inspection of soil site anchoring systems, including stress wave signal testing, processing, and interpretation.